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In this paper, we investigate lepton mass spectra, flavor mixing and CPviolation with a modular $S^{}_4$ symmetry under the assumption that neutrinosare Dirac fermions. We find that the Majorana mass term can be forbidden byadjusting the weight of the right-handed neutrino superfields. We study thescenarios where modular forms in the neutrino sector take the lowestnon-trivial weight two, while those in the charged-lepton sector vary from twoto six. The corrections from renormalization-group running effects to our modelhave also been discussed in detail. We totally obtain twelve different classesof models and find that ten of them can accommodate current neutrinooscillation data.

Dirac neutrino mass models with a modular $S^{}_4$ symmetry